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Matrices- Variable in Matrices-Help

  1. Jan 4, 2012 #1
    Matrices- Variable in Matrices-Help!!!

    1-19-12
    I need help. I have a homework question that I have tried to solve.
    The matrix in the attachment has no inverse. Explain how you can determine the value of x. Then find x.

    I tried cross multiplying.
    3*2/3=4x
    6/3=4x
    2=4x
    x=2/4
    x=1/2
     
  2. jcsd
  3. Jan 4, 2012 #2

    Mark44

    Staff: Mentor

    Re: Matrices- Variable in Matrices-Help!!!

    There is no attachment.
     
  4. Jan 4, 2012 #3
    Re: Matrices- Variable in Matrices-Help!!!

    It say it is attached now.
     

    Attached Files:

  5. Jan 4, 2012 #4

    Mark44

    Staff: Mentor

    Re: Matrices- Variable in Matrices-Help!!!

    The entry at the upper left is -3, not 3.

    Why did you start by cross-multiplying? I'm looking for you to explain why you did what you did.
     
  6. Jan 4, 2012 #5
    Re: Matrices- Variable in Matrices-Help!!!

    My teacher taught me in some cases involving variables we use cross multiplying. I have a text book also that says so.
     
  7. Jan 4, 2012 #6

    micromass

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    Re: Matrices- Variable in Matrices-Help!!!

    Yes, but did your teacher or book also explain why this technique works??
     
  8. Jan 4, 2012 #7
    Re: Matrices- Variable in Matrices-Help!!!

    No neither did.
     
  9. Jan 4, 2012 #8

    micromass

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    Re: Matrices- Variable in Matrices-Help!!!

    Do you know about determinants??
     
  10. Jan 4, 2012 #9
    Re: Matrices- Variable in Matrices-Help!!!

    Yes. The thing is I am in 8th grade doing 11th grade honors Algebra 2.
     
  11. Jan 4, 2012 #10

    micromass

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    Re: Matrices- Variable in Matrices-Help!!!

    OK, what do determinants say about a matrix being invertible??
     
  12. Jan 4, 2012 #11
    Re: Matrices- Variable in Matrices-Help!!!

    I do not know. I know the determinent is a real number that can be computed from elements by a specific formula.
     
  13. Jan 5, 2012 #12

    eumyang

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    Re: Matrices- Variable in Matrices-Help!!!

    Just out of curiosity, what is the author and publisher of your book?
     
  14. Jan 5, 2012 #13
    Re: Matrices- Variable in Matrices-Help!!!

    do you understand what a matrix does?
    what the span of a matrix is?
    and if so, do you understand why a matrix would be singular?
    it's better to understand what things actually do rather than to remember some rules about them

    edit;
    I really dislike this way of teaching the subject (I only know from books, I've never had any formal education in maths), the determinant is an interesting little fellow with sets of properties which can give you information about the matrix when computed.
    What you are doing when you do the cross multiplication is using one of these properties of the determinant, specifically one that gives information about the linear dependancy of the vectors in the c-space of the matrix which by extention tells you about it's invertibility.

    I'll reffer you to an opencourseware lecture that MIT did;


    That whole course is a pretty good introduction to linear algebra in general and Gilbert Strang is quite good at teaching imo.
     
    Last edited by a moderator: Sep 25, 2014
  15. Jan 5, 2012 #14

    Mark44

    Staff: Mentor

    Re: Matrices- Variable in Matrices-Help!!!

    I would guess that the OP isn't this far along in his/her studies of linear algebra.
    More to the point, a square matrix is invertible (i.e., has an inverse) if and only if its determinant is nonzero. The concepts of vectors and linear dependence of the column space are likely too advanced for this poster, IMO.
     
    Last edited by a moderator: Sep 25, 2014
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